The Drei Programming Language: Big step semantics LAMP EPFL

Name

a, b

Integer n Unary operator unop ::= − | ! Binary operator binop ::= + | − | ∗ | / | % | == | != | < | ≤ | > | ≥ |∧ Term

t, t0

Statement

S, S 0 ::= | | | | | | |

Values

v

::= I(n) | ∅

integers unit

Frame

σ

::=  | a→ 7 v, σ

empty frame

Stack

Σ

::=  | σ; Σ

empty stack

::= | | | | | | |

n a unop t t binop t0 readInt readChar {S t} empty

integer literal variable, current instance unary operation binary operation read integer read character block unit

while t S if t then S else S 0 var a : T = t set a = t do t printInt(t) printChar(t) {S}

loop conditional local variable variable assignment instruction print integer print character sequence

Fig. 1. Imperative fragment of Drei

def

def

J−K(n) = −n ( 1 def J!K(n) = 0 ( 1 def J∧K(n1 , n2 ) = 0

J+K(n1 , n2 ) = n1 + n2 def

if n = 0 otherwise

J−K(n1 , n2 ) = n1 − n2 def

if n1 ∗ n2 6= 0 otherwise

J∗K(n1 , n2 ) = n1 ∗ n2 def

J/K(n1 , n2 ) = n1 /n2 def

J%K(n1 , n2 ) = n1 mod n2

Fig. 2. Arithmetic and logical operations on integers ( def

JK(n1 , n2 ) = J